Subj:.....Band Around The Earth (S595b)           From: Yahoo! Answers on 6/14/2009 Drawing from CDC.gov...

Suppose that the surface of the earth is smooth and spherical
and that the distance around the equator is 25,500 miles.  A
steel band is made to fit tightly around the earth at the
equator, then the band is cut and a piece of band 21 feet
long is inserted.  Then the separation of the band from the
earth is spread evenly around the earth.

Can you slide a piece of paper between the band and the earth?
Can a mouse crawl between the band and the earth?  Can a small
dog go between the band and the earth?  To the nearest inch,
what will be the gap, all the way around, between the band and
the earth's surface? (Use 3.14 as an approximate value of Pi)
 
 
 
 

                  THE SOLUTION

It doesn't matter the size of the smooth sphere.  Whether it
is a golf ball, basketball, or the earth, if you increase the circumference of a circle by 21 feet, the radius will increase
by 21 /2*Pi.  If we have to use Pi=3.14, then the radius is
increased by 3.3439 feet or 40.12 inches.  That will be the
gap you will have all around: 40 inches.

Here is the math:

In the original band  C = 2 pi r

so the original radius was r =  C 
                               2 pi

In the new band its length was C + 21, so C + 21 = 2 pi r

so the new radius is r =  C  +  21 
                         2 pi  2 pi

The new radius is increased by 21/2pi or 3.3 feet or 40.1 inched.

The sheet of paper, the mouse and the dog can all fit between
the band and the earth because it is about 40 inches above the earth.